...I will try to see this objectively from both sides.
First of all, I'm not ordinarily inclined to recommend Omega for service of vintage watches due to the extreme cost. However, for some rare and valuable models, they may be the only ones with access to parts. Certainly after 2015, that's going to be the case when Swatch ceases to sell parts to independent watchmakers.
Here's what I think happened over in Switzerland. Omega likely received your watch, logged it in, assigned it to a technician to inspect and also to write a report for the purposes of computing an estimate on repair. In doing so, they likely discovered what you already knew -- that the winding stem was broken and the crystal was no longer water resistant. These parts are relatively inexpensive and they just went ahead and did those replacements without being asked.
IMO, it would be impossible for anyone to properly diagnose any issues with your watch without doing a thorough inspection of the movement. Anytime this is done to a vintage watch, there is a risk of creating additional issues which may not have been evident before such an inspection. If you had chosen to let Omega proceed, the "start-stop" issue should have been routinely fixed. However, since you chose not to have Omega do the work, they put the watch inside one of their service boxes (for shipping safety) and sent it back to the Boutique.
The crystal may have been compromised and no longer moisture resistant and as you stated, the stem needed replacement anyway. I once sent a rare watch to Omega in New York simply to have a cracked crystal replaced which was not available from anyone else. They did no other work (as the watch had been serviced and was operating properly) and sent the watch back in the same red travel box. I was thrilled that they would do that for me.
Things like crystals, stems and crowns are considered to be wear and tear items. Replacing them with the proper OEM parts generally does not detract from value or function. If anything, it enhances them by providing additional environmental protection for the dial. This is where most of the value resides in an expensive vintage watch like a ProPlof. It's no different that replacing tires or changing the oil in a classic car.
My thought would be to go ahead and find a good local independent watchmaker to re-inspect the watch before beating up Omega. It may very well be that a routine service (that you say the watch required anyway) will clear up the issue you are having. If not, then you will be justified in going after Omega.
Then you will be good to go for a good, long time.
gatorcpa